A number of algorithms have been developed for three-dimensional (3D) deconvolution of fluorescence microscopical images. These algorithms use a mathematical-physics model for the process of image formation and try estimate the specimen function, i.e. the distribution of fluorescent dye in the specimen. To keep the algorithms tractable and computational load practical, the algorithms rely on si...

A well-developed phase modulation method is utilized to design a nanogroove grating for a desired diffraction process, which gives rise to the conversion of a surface plasmon wave to an Airy-like radiation beam. Experiments and simulations revealed the unique characteristics of the generated Airy-like beam, such as nonspreading, self-bending, and self-healing. Our result confirms the validation...

The Airy gas model of the edge electron gas is used to construct an exchange-energy functional which is an alternative to those obtained in the local density and generalized gradient approximations. Test calculations for rare gas atoms, molecules, solids and surfaces show that the Airy gas functional performs better than the local density approximation in all cases and better than the generaliz...

The quantum version of the free fall problem is a topic often skipped in undergraduate mechanics courses, because its discussion usually requires wavepackets built on Airy functions—a difficult computation. Here, contrary, we show that can be nicely simplified both for single particle and general many-body systems by making use gauge transformation corresponds to change reference frame from lab...

Closed form solutions are obtained for a Fokker-Planck model for cell growth as a function of maturation velocity and degree of maturation. For reproduction rules where daughter cells inherit their parent's maturation velocity the complete solution is derived in terms of Airy functions. For more complicated reproduction rules partial results are obtained. Emphasis is given to the relationship o...

We study circular nanomechanical graphene resonators by means of continuum elasticity theory, treating them as membranes. We derive dynamic equations for the flexural mode amplitudes. Due to the geometrical nonlinearity the mode dynamics can be modeled by coupled Duffing equations. By solving the Airy stress problem we obtain analytic expressions for the eigenfrequencies and nonlinear coefficie...

The one-dimensional totally asymmetric simple exclusion process (TASEP) is considered. We study the time evolution property of a tagged particle in the TASEP with the step initial condition. Calculated is the multi-time joint distribution function of its position. Using the relation of the dynamics of the TASEP to the Schur process, we show that the function is represented as the Fredholm deter...

The one-dimensional totally asymmetric simple exclusion process (TASEP) is considered. We study the time evolution property of a tagged particle in TASEP with the step-type initial condition. Calculated is the multi-time joint distribution function of its position. Using the relation of the dynamics of TASEP to the Schur process, we show that the function is represented as the Fredholm determin...